Questions tagged [quantum-chemistry]

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Multi-electron Bloch bundles over powers of the Brillouin torus?

The quantum states of single electrons in a crystal famously form a (Hilbert) vector bundle over the Brillouin torus ${\mathbb{T}}^d$ -- the Bloch bundle. Does this theory usefully generalize to ...
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Finding a bound on ground state energy derivatives of molecule

Part of a project I'm working on involves exploring the smoothness of the ground state energy $E(x)$ of a molecule where $E$ is parameterized by the geometry of the molecule. In particular, my goal ...
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What is the single active electron approximation?

I keep stumbling upon this approximation while reading papers on atomic physics, but I couldn't find a proper description of what it is in any textbook or pedagogical paper. The closest I could find ...
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QM: How do electrons affect each other's potential energy?

I'm trying to learn quantum mechanics. And I'm confused. The question is, do electrons affect each other's wave functions, i.e. potential energies? How do they affect each other orbital shapes, how do ...
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The uncertainty principle and the quantization of electron momentum in orbitals - Why are larger energy gaps considered more uncertain?

I am a chemist trying to understand how the uncertainty principle can be applied to the mechanics of atomic and molecular orbitals in order to have better intuitions about stability and reactivity. ...
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Are the concepts of activation energy and collision theory applicable for this reaction?

This is the reaction: $$\text{2Na(s)}+\text{Cl}_2\text{(g)}\longrightarrow \text{2NaCl(s)}\tag{1}$$ This is a reaction between a solid (sodium metal) and a gas (chlorine gas). According to Britannica, ...
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Is ionization energy non-negotiable?

$$\text{2Na(s)}+\text{Cl}_2\text{(g)}\longrightarrow \text{2NaCl(s)}\tag{1}$$ This is a spontaneous reaction ($\Delta G<0$). 2 Na atoms donate 2 electrons to 2 Cl atoms. However, Na still has a ...
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How does the concept of activation energy work for interatomic collisions?

Say we have a Lennard-Jones -esque potential for colliding atoms. Say this potential admits a bound state at a lower energy than the kinetic energy of the colliding atoms. So forming this molecule ...
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Does the copper normalize?

I am reading Concepts of Elemental Particle Physics. In it, it describes what happens when a high energy muon is shot into a copper rod. An electron is is knocked out of its orbit and and photons ...
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Excitation of electrons from $3p$ to $3d$ in sulphur

In my book it is shown that sulphur in its excited state forms 6 covalent bonds with Fluorine to form SF6 but after the electron is excited does it not dexcite from $3d$ back to $3p$ and $3s$ by ...
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Why do some atoms like Mg have several ionization energy levels?

In Dopant Energy Levels in Crystalline Silicon (which asks for a password, but is partially readable if you click "cancel") appears the following image and caption: Figure 2777b shows the ...
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Schrodinger operator with matrix potential and Green's function

Clearly Schrodinger operators with matrix potentials appear very naturally in molecular dynamics/quantum chemistry, particularly when considering a crude adiabatic basis or diabatic basis for an ...
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Why is octaoxygen diamagnetic?

I tried considering that according to LCAO-MO theory $O_2$ is paramagnetic, which is confirmed by experimental evidence. Since octaoxygen has the crystal structure in figure, I thought there is a kind ...
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On non-existence of molecular helium (and or why that's equivalent to bond order zero)

Why does molecular orbital theory (MOT) imply that molecular helium does not exist? All answers I found in the web use following two standard arguments, but I not see why these are sufficient to ...
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Who first modelled water as a tetrahedron?

Who first modelled water as a tetrahedron? In this model the oxygen is at the center and the two hydrogens are at the vertices (I think, or maybe somewhere along the edges?). Source This gives the ...
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What prevents us from designing material or catalysts to meet the custom requirements? [closed]

From the perspective of physics, everything is made of atoms, ions, electrons, etc. Since we know the basic interaction between elementary particles, it might be possible to design customized ...
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1 answer
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Atom orbitals physics vs. chemistry

Why draw chemists always $|2p_x\rangle$, $|2p_y\rangle$ and $|2p_z\rangle$ orbitals instead of $|2,1,m\rangle$? Since $|2p_x\rangle$ or $|2p_y\rangle$ are a superposition of energy eigenstates they ...
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Ultra-Low Temperature semiconductors

What benefits does cooling semiconductors have for technology or any other innovations? I understand semiconductors can become good conductors at high temperatures which are ideal for everyday things ...
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Why does inversion symmetry disallow valence band maximum (VBM) to conduction band minimum (CBM) electronic transitions?

I have somewhere read that due to inversion symmetry in the crystal structure the electronic transition occurs from some bands below VBM and therefore optical band gap comes into the picture with a ...
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1 answer
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Cooperative orders

I am familiar with the more "traditional" types of order and their corresponding degrees of freedom one might find in a many-body system, such as crystalline (translational d.o.f.), ...
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What steps are exact in Born-Oppenheimer and adiabatic approximation?

I am reading about adiabatic and Born-Oppenheimer approximation and I can't understand what steps are exact and what steps are approximations. Both these approximations are based on the idea that as ...
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1 answer
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Quantum mechanical model of benzene ring [closed]

The infinite square well scenario can be used to model the $\pi$-electrons of a benzene ring. It can be shown that the eigenfunctions of the ring can be written as $\Psi_{n}(x) = \frac{1}{\sqrt{L}}e^{\...
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Solving to get the kinetic energy integral for restricted closed shell hartree fock calculations

The Kinetic energy integral given in the book Modern Quantum Chemistry by Attila Szabo and Neil Ostlund is given by (Appendix A eqn A.10) $$ \left(A\left|-\frac{1}{2} \nabla^{2}\right| B\right)=\int d ...
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1 vote
1 answer
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Why does a neutral atom have no external electric field?

I've been trying to find an answer to this for some time now. In advance, I imagine the orbital model, nevertheless I cannot imagine that if I am for example closer to a side of the atom, the dipole ...
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Showing that the creation operator is a spin tensor operator

In the second quantization formalism of quantum chemistry, according to the book 1 on page 43, the creation operators $a_{p,\beta}^{\dagger},a_{p,\beta}^{\dagger}$ satisfy the relations $[\hat S_\pm,...
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How to express atomic states 1S, 1D, 3P in terms of spherical harmonics or cubic harmonics?

Textbook state that, because of Pauli principle and anti-symmetry of wave-function, only 1S, 3P, 1D with totally $C_6^2=15$ states are allowed for 2 electrons $np^2$ state. My question is how to ...
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A poorly posed time dependent perturbation benzene type ring question

In my first year masters QM class my professor recently mentioned an example that he said he would either give on an assignment or possibly put on our exam. We have all our assignments now and it hasn'...
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Probabilities fall outside the differential?

A few years ago I had a conversation with a physical chemist, and one of her comments still lingers in my memory. Our conversation was about Quantum Chemistry. In response to my commenting on the ...
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What do chi ($χ$), psi ($ψ$), and capital gamma ($Γ$) stand for in these equations about molecular geometry (combination bands and overtones)?

Special case If one of the symmetries is doubly degenerate in the excited state a recursion formula is required to determine the symmetry of the $v$th wave function, given by, $$\chi _{v}(R) = \frac{1}...
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Implementing symmetry in MRCI calculation

I am running Multi Reference Configuration Interaction calculations for Aluminium Flouride molecule in its A1Pi state interacting with Helium. For a complete Potential energy surface, i am doing the ...
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1 answer
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Can different electron orbitals within the same atom be entangled?

Could the electron in the outer shell orbital be entangled with an electron within the inner S orbit of the atom? If so, how would this affect the properties of such an atom, such as emission and ...
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2 votes
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In molecular orbital theory for $H_2^+$, why do we only add or subtract orbitals but never alter one of the phases of the orbitals?

EDIT and TLDR: Atkins' physical chemistry contains the quote "In general, from N atomic orbitals we can build N molecular orbitals". In the case of $H^+_2$, we use a combination of N=2 ...
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Relation between Photochemical reactions and Photoelectric effect

I was writing my lab report of determining the value of Planck's Constant using photoelectric effect. Suddenly, a question stuck my mind that in photoelectric effect electrons are ejected from ...
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1 vote
1 answer
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Quantum mechanical description of how bonding works?

I am trying to conceptualize of chemical bonding, and really be able to explain to someone with lots of questions how exactly it works. I am having a hard time conceptualizing what the bonding is ...
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1 vote
1 answer
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Relationship between quantum chemistry and physics Hartree-fock approaches

In standard quantum chemistry books (e.g., Szabo Ostlund), Hartree-Fock is usually introduced from a first quantized picture. Given molecular orbitals $\psi_a(\mathbf{r})$ that are expanded in terms ...
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2 answers
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Why energy expectation values (Energy) are functions of coefficients of corresponding trial wave functions in variational principle?

The method consists of choosing a "trial wavefunction" depending on one or more parameters and finding the values of these parameters for which the expectation value of the energy is the ...
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Doing chemistry with atoms or "Renormalization group on chemistry"

When I studied molecular mechanics we saw all of this in terms of electrons with classical nucleus. Is there a formulation in term of atoms-as-particles (ignoring internal structure, but maybe taking ...
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Ionization potential for surfaces

For an isolated structure, like a molecule, the ionization potential can be computed using total energies obtained from DFT: $$IP = E(N) - E(N-1).$$ But what if I have a structure finite in one ...
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3 votes
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Computing the 2-electron Reduced Density Matrix (2RDM) using QED

So in quantum chemistry there is this concept of the 2-electron Reduced Density Matrix (2RDM), denoted here as $\Gamma$. It is defined, more like a function than a matrix, as the ridiculous integral ...
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Why does the energy of an atomic orbital depend on the proximity to charges?

I was recently reading about Crystal field theory and especially crystal field splitting in the context of transition metals in coordination complexes. Here is what I think I have understood – or what ...
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Calculating the Franck-Condon Factors

I want to calculate the Frank-Condon Factors using the standard equation: $$q_{v'v''}=\left[\int \psi_{v'}^* \psi_{v''} dr\right]^2$$ I have the vibrational wave functions of $v'$ and $v''$ in ...
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Transition Dipole Moment Function

A simple question: I have came across the word "transition dipole moment function" many times. I have seen it in Einstein coefficient relation or also called transition rates. In this ...
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7 votes
4 answers
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Are all waves periodic?

I'm studying waves, and I am confused about two different definitions of a wave. One place defines a wave as "a propagating dynamic disturbance of one or more quantities". Another says that &...
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1 vote
0 answers
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Linear combination of atomic orbitals

For example, I have linear combination of states $$|n,l,m\rangle:~| \psi \rangle = c_1 |2,1,0\rangle + c_2 |2,1,-1\rangle +c_3 |2,1,1\rangle $$. Here $n =2$, $l = 1$, so it's three p-orbitals with ...
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2 answers
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Can ionic bonds only have discrete distances?

If 2 atoms have an ionic bond, can they only be certain distances apart just like an electron can only be in discrete shells around the nucleus? In other words, are ionic bonds quantum?
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4 votes
3 answers
297 views

Why do molecules behave classically at high temperatures?

In chapter 6 of "Charge and Energy Transfer Dynamics in Molecular Systems", the authors consider diatomic molecules in contact with a heat bath. We have established before that the nuclear ...
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What is the IRREP of the $p_z$ orbital in a $C_s$ point group?

What is the representation on the $p_z$ orbital in a $C_s$ symmetry group? The $C_s$ symmetric group has two irreducible no. of representations $A^{'}$ ---> $s, x, y, xy$ and $A^{''}$ ---> $...
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Second quantization for atomic or molecular models

I'm trying to learn QED in the context of quantum chemistry (ie to model relativistic effects for heavy atoms) and I'm struggling conceptually with second quantization: specifically, what is the ...
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Why does the transmission of a material depend on its wavelength?

my question is pretty much in the title 'Why does the transmission of a material depend on its wavelength?' I know it's to do with electrodynamics and solid-state physics. I was just hoping someone ...
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1 answer
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Lagrangian of a Hydrogen Atom

So in classical mechanics, we can generally convert from the Hamiltonian to the Lagrangian and back using Legendre transformations. However, I have found this to be a bit troublesome in QM. ...
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